Tunable cylindrical lenses and head-mounted display including the same

ABSTRACT

Systems include three optical elements arranged along an optical axis each having a different cylinder axis and a variable cylinder refractive power. Collectively, the three elements form a compound optical element having an overall spherical refractive power (SPH), cylinder refractive power (CYL), and cylinder axis (Axis) that can be varied according to a prescription (Rx).

CLAIM OF PRIORITY

This application is a National Stage Application of InternationalApplication No. PCT/US2021/045110, filed Aug. 6, 2021, which claimspriority under 35 USC § 119(e) to U.S. Patent Application Ser. No.63/062,746, filed on Aug. 7, 2020, the entire contents of which arehereby incorporated by reference.

FIELD OF THE DISCLOSURE

The disclosure relates to tunable lenses and more specifically, tohead-mounted displays incorporating tunable lenses to correct forrefractive error of a user.

BACKGROUND

Wearable display systems for augmented reality can include one or twoeyepieces through which a user can view the world and with which thedisplay system can project digital imagery to the user. Eyepieces areoften formed using highly refractive materials and are typicallydesigned to account for users with emmetropic vision, i.e., with norefractive error.

For users with non-emmetropic vision, such as short sighted (myopic) orfar sighted (hyperopic) users, custom inserts can be provided in thewearable display that correct for a user's refractive error, e.g.,according to their ophthalmic prescription (Rx). Alternatively, thedisplay's form factor can be designed to accommodate eyeglasses betweenthe wearer and the display's eyepiece. However, customization of theheadset can be both time-consuming and expensive and form factors thataccommodate eyeglasses can be unwieldy and aesthetically unappealing.

SUMMARY

This disclosure features a tunable lenses that can be integrated into aneyepiece of a head mounted display for the correction of non-emmetropicvision, particularly in a virtual reality head mounted display. Theeyepiece can include a fully integrated, field-configurable opticarranged with respect to a waveguide used to project digital imagery tothe user, the optic being capable of providing a tunable Rx for the userincluding variable spherical refractive power (SPH), cylinder refractivepower (CYL), and cylinder axis (Axis) values. In certain configurations,each tunable eyepiece includes two variable compound lenses: one on theuser-side of the waveguide with variable sphere, cylinder, and axis; anda second on the world side of the waveguide with variable sphere.Collectively, the variable compound lenses can correct for refractiveerror of the user, including astigmatism, and can position digitalimages at appropriate depth planes relative to the environment andcorresponding to the user depth-of-fixation.

In some embodiments, each compound lens is composed of multiple (e.g.,two or three) variable cylindrical lenses. For example, each variablecylindrical lens can include a deformable refractive element integratedwith an actuator. The actuators apply forces to the deformablerefractive elements to vary the curvature of one or two surfaces of thelens, thereby varying the optical power of the cylindrical lens. Anassembly of two such variable cylindrical lenses whose cylinder axes areoriented at right angles can be used to provide a compound lens withadjustable spherical power. An assembly of three variable cylindricallenses whose cylinder axes are oriented at 60° intervals can be used toprovide a compound lens with adjustable SPH, CYL, and Axis.

In a first aspect, disclosed herein is a system, including: a firstoptical element including a first refractive element arranged along anoptical axis, and a first actuator arranged to vary a cylinderrefractive power of the first refractive element in response to a firstcontrol signal, the first refractive element having a first cylinderaxis associated with the first refractive element along a first radialdirection orthogonal to the optical axis; a second optical elementincluding a second refractive element arranged along the optical axis,and a second actuator arranged to vary a cylinder refractive power ofthe second refractive element in response to a second control signal,the second refractive element having a second cylinder axis associatedwith the second refractive element along a second radial directionorthogonal to the optical axis; a third optical element including athird refractive element arranged along the optical axis, and a thirdactuator arranged to vary a cylinder refractive power of the thirdrefractive element along a third radial direction orthogonal to theoptical axis in response to a third control signal, where the first,second, and third radial directions are different; and an electroniccontroller in communication with the first, second, and third actuators,the electronic controller being configured, during operation, to providethe first, second and third control signals to the first, second, andthird actuators, respectively, so that the first, second, and thirdrefractive elements collectively form an optical element having anoverall spherical refractive power (SPH), cylinder refractive power(CYL), and cylinder axis (Axis) according to a prescription (Rx).

In some implementations, an angular separation between the first andsecond radial directions can be equal to an angular separation betweenthe second and third radial directions. For a Cartesian coordinatesystem orthogonal to the optical axis, the first radial direction can beat 30°, the second radial direction can be at 90°, and the third radialdirection can be at 150°. The first cylinder refractive power, C₃₀, thesecond cylinder refractive power, C₉₀, and the third cylinder refractivepower, C₁₅₀, and values for S, C, and A are related according to theformulae:

$C_{30} = {{\frac{2}{3}S} + {\left( {{\frac{2}{3}\cos^{2}A} + {\frac{2\sqrt{3}}{3}\cos\ A\ \sin A}} \right)C}}$$C_{90} = {{\frac{2}{3}S} + {\left( {{\sin^{2}A} - {\frac{1}{3}\cos^{2}A}} \right)C}}$$C_{150} = {{\frac{2}{3}S} + {\left( {{\frac{2}{3}\cos^{2}A} - {\frac{2\sqrt{3}}{3}\cos\ A\ \sin A}} \right)C}}$

At least one of the refractive elements can include a deformable opticalmaterial. The deformable optical material can be a solid opticalmaterial. The solid optical material can be an elastomeric material. Theelastomeric material can be a silicone elastomer. The at least one ofthe refractive elements can include a deformable transparent membraneadjacent the deformable optical material, the actuator of the at leastone refractive element being arranged to deform a shape of thedeformable transparent membrane to vary the cylinder refractive power ofthe at least one refractive element. The actuator bows the membraneabout the cylinder axis of the at least one refractive element to varythe cylinder refractive power of the at least one refractive element.The at least one of the refractive elements can include a rigidtransparent substrate adjacent the deformable optical material on anopposing side of the refractive element from the deformable opticalmaterial. The optical element of the at least one of the refractiveelements can include a rigid gasket at an edge of the deformable opticalmaterial and the deformable transparent membrane pivots on the rigidgasket when acted upon by the actuator. The cylinder refractive power ofeach of the first, second, and third optical elements can be variablethrough a range from −5 D to +5 D. The optical element has an aperturehaving an area of 1 cm² or more. (E.g., 5 cm² or more, 10 cm² or more,16 cm² or more). Each of the refractive elements has a thickness alongthe optical axis of 10 mm or less. (E.g., 6 mm or less, 4 mm or less, 3mm or less, 2 mm or less, 1 mm or less).

Each optical element can include a pair of refractive elements, eachrefractive element of the pairs having a cubic profile oriented along anaxis in the radial direction of the optical element, the actuator of thecorresponding optical element being arranged to slide the pair ofrefractive elements in opposite directions orthogonal to the opticalaxis.

In a second aspect, disclosed herein is a head-mounted display system,including: a first optical element having a variable sphericalrefractive power (SPH); a second optical element having a variable SPH,a variable cylinder refractive power (CYL), and a variable cylinder axis(Axis); a see-through display arranged between the first optical elementand the second optical element; and an electronic controller incommunication with the first optical element, the second opticalelement, and the see-through display, the electronic controller beingprogrammed to adjust the SPH of the first optical element and the SPH,CYL, and Axis of the second optical element according to a prescription(Rx) of an individual user of the head-mounted display.

The head-mounted display can further include a frame for mounting thefirst optical element, second optical element, and see-through displayrelative to each other and, during use, relative to a user of thehead-mounted display. The second optical element can be arranged betweenthe see-through display and the user during use of the head-mounteddisplay. The first optical element can include two variable cylindricallenses having their respective cylinder axes orthogonal to each other.The head-mounted display can further include an eye-tracking module, theelectronic controller being programmed to vary the prescription of thesecond optical element based on information about where a user of thehead-mounted display can be looking from the eye-tracking module. Theelectronic controller can be programmed to vary the SPH, CYL, and Axisof the second optical element from a near-vision prescription to adistance-vision prescription depending on where the user can be looking.The head-mounted display can further include a biometric identificationmodule, the electronic controller being programmed to identify a userbased on information from the biometric identification module and adjusta prescription of the second optical element based on the user'sidentity. The biometric identification module can be an irisidentification module.

Among other advantages, the tunable eyepiece can correct for the uniqueoptical prescription, including astigmatism, of a user while minimizingelectrical power consumption and electro-mechanical overhead. Thetunable eyepiece can alleviate the need to fabricate a custom rigideyepiece for each user and increase the availability of mixed realityproducts users with non-emmetropic vision. An included biometric modulecan identify a user based on their unique iris pattern and adjust thetunable eyepieces to adjust to the prescription of multiple users in thefield.

Other advantages will be apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a wearable headset display.

FIG. 2 is a schematic diagram representing the placement of an eyebehind a tunable eyepiece with proximal and distal tunable opticalelements.

FIG. 3A is a diagram of compound lens used to correct for non-emmetropicvision including a spherical and a cylindrical lens.

FIG. 3B is a diagram of three cylindrical lenses representing analternative means to correct for non-emmetropic vision.

FIG. 4A is a schematic diagram depicting an edge-view of an unactuatedexemplary refractive element.

FIG. 4B is a schematic diagram depicting an edge-view of an exemplaryrefractive element combined with an actuator in register with thegasket.

FIG. 5A is a perspective view of three components of a refractiveelement in a plano configuration.

FIG. 5B is a perspective view of the refractive element components shownin FIG. 5A actuated to provide positive cylindrical power.

FIG. 5C is a perspective view of the refractive element components shownin FIG. 5A actuated to provide negative cylindrical power.

FIG. 6 is a schematic diagram of six paired refractive elements withmirrored cubic profiles in a sliding configuration.

In the figures, like symbols indicate like elements.

DETAILED DESCRIPTION

FIG. 1 illustrates an example head-mounted display system 60 thatincludes a see-through display 70, and various mechanical and electronicmodules and systems to support the functioning of that display 70. Thedisplay 70 is housed in a frame 80, which is wearable by a displaysystem user 90 and which is configured to position the display 70 infront of the eyes of the user 90. The display 70 may be consideredeyewear in some embodiments. In some embodiments, a speaker 100 iscoupled to the frame 80 and is positioned adjacent the ear canal of theuser 90. The display system may also include one or more microphones 110to detect sound. The microphone 110 can allow the user to provide inputsor commands to the system 60 (e.g., the selection of voice menucommands, natural language questions, etc.), and/or can allow audiocommunication with other persons (e.g., with other users of similardisplay systems). The microphone 110 can also collect audio data fromthe user's surroundings (e.g., sounds from the user and/or environment).In some embodiments, the display system may also include a peripheralsensor 120 a, which may be separate from the frame 80 and attached tothe body of the user 90 (e.g., on the head, torso, an extremity, etc.).The peripheral sensor 120 a may acquire data characterizing thephysiological state of the user 90 in some embodiments.

In some embodiments, the display system may also include an eye-trackingmodule 125 a. In some embodiments, the eye-tracking module 125 a caninclude a biometric identification module to acquire biometric data ofthe user 90. In some embodiments, the biometric identification modulecan be an iris identification module.

In some embodiments, the eye-tracking module 120 a may acquiredepth-of-fixation data. The eye-tracking module 120 a may be operativelycoupled by communications link 125 b (e.g., a wired lead or wirelessconnectivity) to the local processor and data module 140. Theeye-tracking module 120 a may communicate the biometric anddepth-of-fixation data to the local processor and data module 140.

The display 70 is operatively coupled by a communications link 130, suchas by a wired lead or wireless connectivity, to a local data processingmodule 140 which may be mounted in a variety of configurations, such asfixedly attached to the frame 80, fixedly attached to a helmet or hatworn by the user, embedded in headphones, or removably attached to theuser 90 (e.g., in a backpack-style configuration or in a belt-couplingstyle configuration). Similarly, the sensor 120 a may be operativelycoupled by communications link 120 b (e.g., a wired lead or wirelessconnectivity) to the local processor and data module 140. The localprocessing and data module 140 may include a hardware processor, as wellas digital memory, such as non-volatile memory (e.g., flash memory or ahard disk drive), both of which may be utilized to assist in theprocessing, caching, and storage of data. The data may include data 1)captured from sensors (which may be, e.g., operatively coupled to theframe 80 or otherwise attached to the user 90), such as image capturedevices (e.g., cameras), microphones, inertial measurement units,accelerometers, compasses, GPS units, radio devices, gyros, and/or othersensors disclosed herein; and/or 2) acquired and/or processed using aremote processing module 150 and/or a remote data repository 160(including data relating to virtual content), possibly for passage tothe display 70 after such processing or retrieval. The local processingand data module 140 may be operatively coupled by communication links170, 180, such as via a wired or wireless communication links, to theremote processing module 150 and the remote data repository 160 suchthat these remote modules 150, 160 are operatively coupled to each otherand available as resources to the local processing and data module 140.In some embodiments, the local processing and data module 140 mayinclude one or more of the image capture devices, microphones, inertialmeasurement units, accelerometers, compasses, GPS units, radio devices,and/or gyros. In some other embodiments, one or more of these sensorsmay be attached to the frame 80, or may be standalone devices thatcommunicate with the local processing and data module 140 by wired orwireless communication pathways.

The remote processing module 150 may include one or more processors toanalyze and process data, such as image and audio information. In someembodiments, the remote data repository 160 may be a digital datastorage facility, which may be available through the internet or othernetworking configuration in a “cloud” resource configuration. In someembodiments, the remote data repository 160 may include one or moreremote servers, which provide information (e.g., information forgenerating augmented reality content) to the local processing and datamodule 140 and/or the remote processing module 150. In otherembodiments, all data is stored and all computations are performed inthe local processing and data module, allowing fully autonomous use froma remote module.

Variable eyepiece components included with the eyepiece of a displayadjust the refractive power of the eyepiece in order to match the depthof the fixation for a user with the user's vision. The refractive powerof the variable components can be set at different values across a rangeof possible values, performing the function of fixed lenses with theadded flexibility of controllable correction. The optical prescription(Rx) of a user for correcting refractive error can be loaded into theheadset controller and the variable components modified to correct forthe unique set of parameters within. The headset can perform thismodification for each new user, correcting for each unique Rx in turn.

Referring to FIG. 2 , an eyepiece 200 of a head-mounted display systemdirects light from a projector 220 to the eye 210 of a user. Theprojector 220 and eyepiece 200 are positioned relative to one anotherand to the eye 210 of the user by a frame or housing (not shown). Theprojector 220 is located beside the user's temple and directs light toan end of the eyepiece 200 that extends past the user's temple. Asshown, eyepiece 200 includes a planar waveguide 240, an input couplinggrating (ICG) 230, and out-coupling element (OCE) 250, however, morecomplex arrangements (e.g., composed of multiple stacked waveguides) arepossible. A first variable focus assembly 270 a is located on the worldside of waveguide 240 and a second variable focus assembly 270 b islocated on the user side. Collectively, the refractive powers ofvariable focus assemblies 270 a and 270 b are adjusted to concurrentlycorrect the optical properties of the eyepiece to account for thevirtual image depth plane and the Rx of a user.

ICG 230 is a surface grating positioned to receive light from projector220 and facilitates in-coupling of light from projector 220 into theeyepiece 200. The ICG 230 is located at or close to the edge of theeyepiece 200 closest to the projector 220. The ICG 230 directs the lightfrom the projector 220 into guided modes in the planar waveguidesubstrate 240 of eyepiece 200.

The planar waveguide substrate 240 guide the in-coupled light along theeyepiece 200 through total internal reflection at its surfaces to theout-coupling element (OCE) 250. The OCE 250 is a second surface gratingconfigured to extract the light out of the planar waveguide substrate240 and redirect it towards the eye 210 of the user. The OCE 250 caninclude an exit pupil expander (EPE) or an orthogonal pupil expander(OPE) or both. The OCE 250 is located in front of the user's eye 210,delivering light from the projector to the region in which a pupil 212of the user can be positioned to receive light outputted from the OCE150. This region is termed the eyebox. The OCE 250 can further have alateral dimension to accommodate a range of lateral positions of theeyebox. For example, a non-limiting range of the lateral dimension 251of the OCE 250 can be 30 mm or less (e.g., 25 mm or less, 20 mm or less,15 mm or less).

Variable focus assembly 270 b arranged on the user-facing surface of theeyepiece 200 corrects for the non-emmetropic vision of the user,including for astigmatism. Variable focus assembly 270 b additionallyplaces the focus of the eyepiece 200 at the correct depth plane todisplay virtual images. This placement of the focus also affects thefocus of real images passing through the display to the user. Thevariable focus assembly 270 a arranged on the world-facing surface ofthe eyepiece 200 corrects the real image focus placement resulting fromthe correction of variable focus assembly 270 b. Variable focus assembly270 a includes two optical elements, 271 a and 271 b, and variable focusassembly 270 b includes three optical elements, 271 c, 271 d, and 271 e.

In some embodiments, each optical element 271 a-e includes a refractiveelement incorporating a deformable optical material in contact with adeformable membrane. The refractive elements are coupled to actuators272 a-e, which operate to change the refractive power of the connectedoptical element 271 a-e, described further in FIG. 4 . The actuators272, for example, can deform at least one surface of the correspondingrefractive element along a single axis, thereby causing the refractiveelement of the optical element 271 to perform the function of a variablecylindrical lens. In some embodiments, the actuators can bepiezoelectric actuators.

Actuators 272 a-e apply forces responsive to control signals from thecontroller 274. In certain implementations, the headset controller 274performs the calculations to determine the refractive power for eachoptical element 271 a-e. The lens profile of each optical element 271a-e combine to establish the refractive power of the variable focusassembly 270 a or 270 b. The optical power for the variable focusassemblies can vary based on a variety of considerations, including userRx, user environment, projected imagery, and/or a combination of theseparameters.

In some embodiments, the controller 274 can receive biometric data froman eye-tracking module and adjust the refractive power of variable focusassembly 270 b to correct for the Rx of the user based on theirbiometric identification. In some embodiments, the controller 274 canreceive user depth-of-fixation data from the eye-tracking module andadjust the refractive power of variable focus assembly 270 b to correctfor the near- or distance-vision Rx of a user. Similarly, the controller274 can receive user depth-of-fixation data from the eye-tracking moduleand adjust the lens profile of variable optical element 270 a to adjustthe optical depth of virtual images to match the depth of the fixationfor a user.

In general, a person's eye can have refractive errors that lead toconditions such as myopia, hyperopia, astigmatism, or a combinationthereof. Using corrective lenses to modify the incoming light rayscorrects for these refractive errors. Myopic or hyperopic refractiveerrors occur when the projected image of an eye is out of focus with theback plane of the eye and are typically corrected through lenses with a‘spherical’ profile placed between the eye and incoming light. Broadly,a plano-spherical lens profile can be considered a planar section of thesurface of a sphere resulting in a lens profile with two opposingsurfaces, a curved surface and a planar surface. The curved surface of aspherical lens is radially symmetric around a central axis orientedorthogonally to the planar surface. A lens with a spherical profilearranged along the optical axis of a user's eye corrects for theserefractive errors.

Astigmatism refractive errors are due the eye lens having differentialcurvatures along different directions. A lens having a ‘cylinder’profile can correct this type of error. A plano-cylindrical lens profilecan be considered a planar section of a cylinder taken parallel to thelongitudinal axis of the cylinder. This results in a lens with opposingcurved and planar surfaces (e.g., convex). The longitudinal axis alongthe center of the planar surface is termed the cylinder axis. The curvedsurface has an equal radius of curvature along the length of thecylinder profile.

Typically, a lens having a spherical component and a cylinder componentare used to correct refractive errors of an astigmatic non-emmetropiceye. An ophthalmic prescription (Rx) combines a spherical component, acylindrical component, and a cylinder axis component (SPH, CYL, Axis)which are respectively the refractive powers of a spherical and acylindrical lens, and the orientation of the cylinder axis. A Cartesiancoordinate system oriented orthogonally to the optical axis with 0°directed horizontally can be used to define the cylinder axis.

A spherical or cylindrical lens have respective strengths, or refractivepowers, typically measured in diopters (D). The refractive power of alens can be zero, a negative (e.g., divergence), or a positive (e.g.,convergence) number. Without wishing to be bound by theory, therefractive power can be equal to the reciprocal of the focal length (f),D=1/f. For example, a lens with a refractive power of +3 D bringsparallel rays of light from optical infinity to focus at ⅓ meter. For afurther example, a flat or plano lens has a refractive power of 0 D anddoes not cause light to converge or diverge.

An Rx can be represented by a combination of a spherical lens and acylindrical lens, as shown in FIG. 3A. Depicted is an exemplary assemblyof a spherical lens 310 of refractive power S, and a cylindrical lens312 of refractive power C. The cylinder axis 313 of the cylindrical lens312 is shown oriented at an angle A with respect to a horizontal plane.Without wishing to be bound by theory, the phase profile at a point(x,y) on the surface of any R_(x) is proportional to R_(x)(x, y)∝S(x²+y²)+C (cos Ax+sin Ay)² where S the refractive power of the sphericallens, C is the refractive power of the cylindrical lens, and A is theangular orientation of the cylindrical lens.

The correction power of a spherical lens 310 can be alternativelyachieved by a pair of cylinder lenses 312 whose cylinder axes areoriented at 90° from each other. Accordingly, the combination ofspherical 310 and cylindrical lens 312 shown in FIG. 3A is similarlyachievable through the combination of three cylindrical lenses. FIG. 3Bdepicts the arrangement of three cylindrical lenses 312 a, 312 b, and312 c with their cylinder axes arranged at radial directions of 30°,90°, and 150° from the horizontal plane of the eye, with respectiverefractive powers of C₃₀, C₉₀, and C₁₅₀. Without wishing to be bound bytheory, the refractive powers C₃₀, C₉₀, and C₁₅₀ necessary to correctfor an R_(x) with spherical and cylindrical components can be determinedusing

$C_{30} = {{\frac{2}{3}S} + {\left( {{\frac{2}{3}\cos^{2}A} + {\frac{2\sqrt{3}}{3}\cos\ A\ \sin A}} \right)C}}$$C_{90} = {{\frac{2}{3}S} + {\left( {{\sin^{2}A} - {\frac{1}{3}\cos^{2}A}} \right)C}}$$C_{150} = {{\frac{2}{3}S} + {\left( {{\frac{2}{3}\cos^{2}A} - {\frac{2\sqrt{3}}{3}\cos\ A\ \sin A}} \right)C}}$for each respective lens.

Based on the above, the optical elements 271 a-e described in FIG. 2 canperform the function of cylindrical lenses and they can be oriented andcombined in optical elements to accomplish the desired Rx.

While the arrangement of cylinder axes arranged at radial directions of30°, 90°, and 150° have been described and will function for any threeelement Rx (e.g., SPH, CYL, Axis), these orientations are not the onlysolution capable of providing correction for astigmatic non-emmetropicvision. In general, there are many sets of angles that would givesufficient degrees of freedom to match the three parameters of an Rx.For example, three cylinder axes oriented at 0°, 60°, and 120° (e.g.,from the horizontal plane of the eye) may also correct for such an Rx.This arrangement maintains the 60° separation between cylinder axesdescribed in FIG. 3B. Though as a further example, three cylinder lenseswith cylinder axes separated by 45° (e.g., 0°, 45°, 90°) may alsoprovide the correction necessary for a three element R_(x).

In general, the total angular separation between the three cylinder axesof a set of cylindrical lenses can be sufficient to preclude redundancybetween two or more of the cylinder lenses. For example, the totalangular separation between the three cylinder axes can be in a rangefrom 45° to 180°. The angular displacement of a middle of the threecylinder axes can be approximately equal from the other two cylinderaxes (e.g., for a total angular separation of 90°, the middle axes canbe 45° from the other two) or the cylinder axes can be separated byunequal angles.

In general, a variety of optical elements capable of providing avariable cylindrical lens can be used for the variable focus assembliesdepicted in FIG. 2 . An example is shown in FIGS. 4A and 4B, which showsan optical element 400 composed of a deformable transparent membrane410, a transparent substrate 412, a deformable optical material 414, anda gasket 416 around the edge of the deformable optical material 414.Together, deformable transparent membrane 410, deformable opticalmaterial 414, and substrate 412 form a variable cylindrical lens with anoptical axis 420 orthogonal to the cylinder axis, which extendsperpendicular to the plane of the figure. The thickness of opticalelement 400 is 10 mm or less (e.g., 6 mm or less, 4 mm or less, 3 mm orless, 2 mm or less, 1 mm or less). Relatively thin optical elements canbe desirable, providing a compact, light device suitable forincorporating into a head-mounted display.

Optical element 400 also includes an actuator 472 arranged to change thecylinder refractive power of the optical element.

The deformable transparent membrane 410 is positioned in contact withthe upper rim of the rigid gasket 416 and the upper surface of theoptical material 414. Contact elements of actuator 472 are positioned incontact with the opposite side of membrane 410. The transparent membrane410 is composed of a transparent material capable of deforming (e.g.,bowing) when appropriate force is applied. Example materials includeinorganic glasses, such as borosilicate glass, or plastic films, such asthin film polycarbonate. The thickness of the transparent membrane 410is sufficient to provide protection to the optical material 416 whilestill remaining flexible. For example, the transparent membrane can beabout 0.1 mm or less thick.

The gasket 416 encircles the edge and enclosing the optical material 414to a common height. The gasket 416 contains the lateral expansion andcontraction of the material 414 when the optical element 271 isactuated. The gasket 416 further partially encases the transparentsubstrate 412 to form an aperture through which light passes along theoptical axis 420. In some embodiments, the aperture can be have aviewing area of 1 cm² or more (e.g., 5 cm² or more, 10 cm² or more, 16cm² or more).

Arranged between the substrate 412 and the membrane 410 is thedeformable optical material 414. The optical material 414 is composed ofa low durometer material that is substantially transparent to light atoptical wavelengths. In some embodiments, the optical material can be asolid optical material, such as an elastomeric material. For example,materials such as silicone elastomers or gels can be used for theoptical material 414. Other materials measuring between 10 and 50 on a000-scale Shore durometer can also be considered (e.g., between 10 and40, between 10 and 30, between 10 and 20, between 20 and 50, between 30and 50, or between 40 and 50).

The rigid transparent substrate 412 provides a rigid base for thedeformable optical material 414 and extends across the full interiorwidth of the rigid gasket 416. The rigid transparent substrate 412 iscomposed of a material that retains its shape under the forces appliedby the deformable optical material 414 and is substantially transparentto light at optical wavelengths. For example, the substrate 412 can beformed from plastic or inorganic glass. Substrate 412 can have athickness of 1 mm thick or less (e.g., 0.8 mm or less, 0.6 mm or less,0.4 mm or less, 0.2 mm or less).

In FIG. 4A, the optical element 400 is shown in an unactuated state inwhich the deformable membrane 410 has an infinite radius of curvature,e.g., a refractive power of 0. Upon activation by actuator 472,deformations of the membrane 410 compress or expand the optical material414 thereby changing the refractive power of the optical element.

Referring now to FIG. 4B, actuator 272 mechanism is shown arranged inregister with the rigid gasket 416 and in contact with the outer edge ofthe membrane 410 of the refractive element 400. The actuator 272 pivotson the gasket 416 to apply parallel and co-directional forces therebydeforming the membrane 410 along an axis parallel with and central tothe edges of the gasket 416. The deformation changes the radius ofcurvature of the membrane 410 causing it to bow. The actuator 272 causesthe membrane 410 to be concave or convex, correlating to a positive ornegative refractive power, respectively. The axis around which thedeformations occur is the cylinder axis of the optical element. In theexample of FIG. 4B, the axis extends perpendicular out of the plane ofthe page.

An illustration of these deformations is shown in FIGS. 5A-C. FIG. 5Adepicts a refractive element 500 similar to that depicted in FIGS. 4Aand 4B, showing only the transparent membrane 510, the rigid substrate512, and the optical material 514. A Cartesian coordinate system 530 isshown to the left of FIG. 5A for context. The optical axis forrefractive element 500 is parallel to the z-axis of coordinate system530. A change in the radius of curvature of the membrane 510 withrespect to a cylinder axis 520 orthogonal to the optical axis causescompression or expansion of the optical material 514 resulting in achange in the refractive power of the refractive element 500. The changein the radius of curvature the membrane 510 causes a positive or anegative cylinder refractive power. For example, the cylinder refractivepower can be variable through a range from −5 D to +5 D (e.g., −4 D, −3D, −2 D, −1 D, 0 D, 1 D, 2 D, 3 D, or 4 D). The cylinder refractivepower can be varied in incremental steps of 0.1 D or more (e.g., 0.2 Dor more, such as 0.25D or 0.5D) from −5D to +5D, for example.

While FIG. 5A depicts the refractive element 500 in an unactuated state,FIGS. 5B and 5C depict refractive element 500 in actuated states. FIG.5B shows the refractive element 500 actuated along cylinder axis 520creating a convex plano-cylinder lens. The lens of FIG. 5B provides apositive cylinder refractive power (e.g., 1 D, 2 D, 3 D, or 4 D). FIG.5C shows the same exemplary refractive element 500 actuated to form aconcave plano-cylinder lens providing a negative cylinder refractivepower (e.g., −4 D, −3 D, −2 D, or −1 D).

Other assemblies that operate as variable cylindrical lenses are alsopossible. For example, in another embodiment, a variable focus assemblyis composed of sliding pairs of rigid refractive elements (e.g., moldedor ground elements formed from glass or plastic), in which each pairoperates as a variable cylindrical lens. An example is shown in FIG. 6 ,which depicts a variable focus assembly 600 that includes three pairs620, 621, and 622, of refractive elements. Specifically, pair 620 iscomposed of refractive elements 620 a and 620 b, pair 621 is composed ofrefractive elements 621 a and 621 b, and pair 622 is composed ofrefractive elements 622 a and 622 b. An inset perspective axes is shownorienting the x-, y-, and z-axis of FIG. 6 .

Each refractive element (620 a, b; 621 a, b; and 622 a, b) has a planarsurface and an opposing two-dimensional cubic surface. In general, acubic surface is a surface defined by a polynomial equation of the thirddegree, e.g., a cubic polynomial. A refractive element having a cubicsurface can be constructed by combination of positive and negativecylindrical lenses profiles of similar radii of curvature. The resultingsurface closely follows a cubic polynomial. The cubic surface of onerefractive element of a pair faces the second refractive element of thepair whose cubic surface is the mirror of the first. Pairs of refractiveelements with aligned cubic vertices perform the function of a lens ofzero refractive power. When the cubic vertices of the lenses aretranslationally misaligned, a refractive element will refract lightpassing through onto a focal line, thereby performing the effect of avariable cylindrical lens.

Each pair of refractive elements, for example refractive elements 620 aand 620 b, are separated by a distance that allows the refractiveelements to translate with respect to one another without the cubicsurfaces coming in contact. In the example embodiment of FIG. 6 ,refractive elements 620 a and 620 b are capable of translating along thex-axis by a distance without the cubic surfaces coming in contact. Thisdistance is dependent on the depth of cubic profile of the pairedrefractive elements. Refractive elements 620 a and 620 b, 621 a and 621b, and 622 a and 622 b are generally composed of a rigid transparentmaterial such as an inorganic glass (e.g., a borosilicate glass) or asuitable plastic (e.g., polycarbonate).

Using optical element 620 as a representative example, the totalthickness of optical element 620 can be 10 mm or less, as describedabove, and includes the respective thicknesses of refractive elements620 s and 620 and their separation distance. The cubic profiles ofrefractive elements 620 a and 620 b are oriented along a common radialaxes orthogonal to the optical axis, equivalent to the cylinder axesdescribed above. In this manner, optical element 620 can perform thefunction of a variable cylindrical lens. Optical element 620 is shown incontact with linear actuator 630. Actuators 630 operates to translaterefractive elements 620 a and 620 b in opposite directions along acommon axis orthogonal to the optical axis.

For example, linear actuator 630 can translate refractive elements 620 bwith respect to 620 a to create a positive or a negative refractivepower. Misaligning the mirrored cubic profiles of a refractive elementin one direction will result in positive refractive power (e.g., 1 D, 2D, 3 D, 4 D, or 5 D). Misaligning the mirrored cubic profiles of arefractive element in the opposite direction will result in a negativecylinder refractive power (e.g., −1 D, −2 D, −3 D, −4 D, or −5 D).

The three optical elements 620, 621, and 622 are shown with cylinderaxes corresponding to 150°, 90°, and 30° from the horizontal plane ofthe eye, similar to the lenses of FIG. 3B. Said differently, thecylinder axes are oriented on the x-y plane at 150°, 90°, and 30° fromthe x-axis, respectively. The dashed lines on the cubic surfaces ofrefractive elements 620 b, 621 b, and 622 b are aligned with therespective cylinder axes of optical elements 620, 621, and 622. Eachoptical element 620, 621, and 622, is shown in contact with linearactuators 630, 631, and 632. As described above, any three refractiveelements with their respective cubic profiles corresponding to 150°,90°, and 30° from the horizontal plane of the eye, such as the exemplarysystem of FIG. 6 , performs the correction for the ophthalmicprescription of any user. Similarly, any two such optical elements withcubic vertices oriented at a right angle will perform the function of aspherical lens. For example, such an arrangement can be used to performthe virtual image plane adjustment for variable focus assembly 270 a.

A number of embodiments are described. Other embodiments are in thefollowing claims.

What is claimed is:
 1. A system, comprising: a first optical elementcomprising a first refractive element arranged along an optical axis,and a first actuator arranged to vary a cylinder refractive power of thefirst refractive element in response to a first control signal, thefirst refractive element having a first cylinder axis associated withthe first refractive element along a first radial direction orthogonalto the optical axis; a second optical element comprising a secondrefractive element arranged along the optical axis, and a secondactuator arranged to vary a cylinder refractive power of the secondrefractive element in response to a second control signal, the secondrefractive element having a second cylinder axis associated with thesecond refractive element along a second radial direction orthogonal tothe optical axis; a third optical element comprising a third refractiveelement arranged along the optical axis, and a third actuator arrangedto vary a cylinder refractive power of the third refractive elementalong a third radial direction orthogonal to the optical axis inresponse to a third control signal, where the first, second, and thirdradial directions are different; and an electronic controller incommunication with the first, second, and third actuators, theelectronic controller being configured, during operation, to provide thefirst, second and third control signals to the first, second, and thirdactuators, respectively, so that the first, second, and third refractiveelements collectively form an optical element having an overallspherical refractive power (SPH), cylinder refractive power (CYL), andcylinder axis (Axis) according to a prescription (Rx).
 2. The system ofclaim 1, wherein an angular separation between the first and secondradial directions is equal to an angular separation between the secondand third radial directions.
 3. The system of claim 1, wherein, for aCartesian coordinate system orthogonal to the optical axis, the firstradial direction is at 30°, the second radial direction is at 90°, andthe third radial direction is at 150°.
 4. The system of claim 3, whereinthe first cylinder refractive power, CC₃₀ the second cylinder refractivepower, C₉₀, and the third cylinder refractive power, C₁₅₀, and valuesfor S, C, and A are related according to the formulae:$C_{30} = {{\frac{2}{3}S} + {\left( {{\frac{2}{3}\cos^{2}A} + {\frac{2\sqrt{3}}{3}\cos\ A\ \sin A}} \right)C}}$$C_{90} = {{\frac{2}{3}S} + {\left( {{\sin^{2}A} - {\frac{1}{3}\cos^{2}A}} \right)C}}$$C_{150} = {{\frac{2}{3}S} + {\left( {{\frac{2}{3}\cos^{2}A} - {\frac{2\sqrt{3}}{3}\cos\ A\ \sin A}} \right)C}}$5. The system of claim 1, wherein at least one of the refractiveelements comprises a deformable optical material comprising a solidoptical material.
 6. The system of claim 5, wherein the solid opticalmaterial is an elastomeric material comprising a silicone elastomer. 7.The system of claim 5, wherein the at least one of the refractiveelements comprises a deformable transparent membrane adjacent thedeformable optical material, the actuator of the at least one refractiveelement being arranged to deform a shape of the deformable transparentmembrane to vary the cylinder refractive power of the at least onerefractive element.
 8. The system of claim 7, wherein the actuator bowsthe membrane about the cylinder axis of the at least one refractiveelement to vary the cylinder refractive power of the at least onerefractive element.
 9. The system of claim 7, wherein the at least oneof the refractive elements comprises a rigid transparent substrateadjacent the deformable optical material on an opposing side of therefractive element from the deformable optical material.
 10. The systemof claim 7, wherein the optical element of the at least one of therefractive elements comprises a rigid gasket at an edge of thedeformable optical material and the deformable transparent membranepivots on the rigid gasket when acted upon by the actuator.
 11. Thesystem of claim 1, wherein the cylinder refractive power of each of thefirst, second, and third optical elements is variable through a rangefrom −5 D to +5 D.
 12. The system of claim 1, wherein the opticalelement has an aperture having an area of 1 cm² or more and wherein eachof the refractive elements has a thickness along the optical axis of 10mm or less.
 13. The system of claim 1, wherein each optical elementcomprises a pair of refractive elements, each refractive element of thepairs having a cubic profile oriented along an axis in the radialdirection of the optical element, the actuator of the correspondingoptical element being arranged to slide the pair of refractive elementsin opposite directions orthogonal to the optical axis.
 14. Ahead-mounted display system, comprising: a first optical element havinga variable spherical refractive power (SPH); a second optical elementhaving a variable SPH, a variable cylinder refractive power (CYL), and avariable cylinder axis (Axis); a see-through display arranged betweenthe first optical element and the second optical element; and anelectronic controller in communication with the first optical element,the second optical element, and the see-through display, the electroniccontroller being programmed to adjust the SPH of the first opticalelement and the SPH, CYL, and Axis of the second optical elementaccording to a prescription (Rx) of an individual user of thehead-mounted display.
 15. The head-mounted display of claim 14, furthercomprising a frame for mounting the first optical element, secondoptical element, and see-through display relative to each other and,during use, relative to a user of the head-mounted display.
 16. Thehead-mounted display of claim 14, wherein the second optical element isarranged between the see-through display and the user during use of thehead-mounted display, and wherein the first optical element comprisestwo variable cylindrical lenses having their respective cylinder axesorthogonal to each other.
 17. The head-mounted display of claim 14,further comprising an eye-tracking module, the electronic controllerbeing programmed to vary the prescription of the second optical elementbased on information about where a user of the head-mounted display islooking from the eye-tracking module.
 18. The head-mounted display ofclaim 17, wherein the electronic controller is programmed to vary theSPH, CYL, and Axis of the second optical element from a near-visionprescription to a distance-vision prescription depending on where theuser is looking.
 19. The head-mounted display of claim 14, furthercomprising a biometric identification module, the electronic controllerbeing programmed to identify a user based on information from thebiometric identification module and adjust a prescription of the secondoptical element based on the user's identity.
 20. The head-mounteddisplay of claim 19, wherein the biometric identification module is aniris identification module.